Cooper Instability of Composite Fermions

Abstract

When confined to two dimensions and exposed to a strong magnetic field, electrons screen the Coulomb interaction in a topological fashion; they capture and even number of quantum vortices and transform into particl es called `composite fermions'. The fractional quantum Hall effect occurs in such a system when the ratio (or `filling factor', $ν$) of the number of electrons and the degeneracy of their spin-split energy states (the Landau levels) takes on particular values. The Landau level filling $ν=1/2$ corresponds to a metallic state in which the composite fermions form a gapless Fermi sea. But for $ν=5/2$, a fractional quantum Hall effect is observed instead; this unexpected result is the subject of considerable debate and controversy. Here we investigate the difference between these states by considering the theoretical problem of two composite fermions on top of a fully polarized Fermi sea of composite fermions. We find that they undergo Cooper pairing to form a p-wave bound state at $ν=5/2$, but not at $ν=1/2$. In effect, the repulsive Coulomb interaction between electrons is overscr eened in the $ν=5/2$ state by the formation of composite fermions, resulting in a weak, attractive interaction.